1. Having candidates review each other seems like a good way to have the worst candidates float to the top. If you're in a contest with your competitors, given the option to knock the best options out of the race, wouldn't you do so? It seems like you're taking an overly optimistic view of human nature.
2. Having a large portion of the election based on randomness seems like it would diminish voter turnout even further. I understand its an attempt to reduce the noise created by the surrounded hype of a candidate, and that it would cause people to research these people on their own, but I dont think that would happen. I think people would see 2 random people, have no interest in either of them at a surface value, and then not vote as a result.
3. I dislike your criteria for selecting candidates, particularly for financial value. I don't think that a wealthy person is necessarily any more qualified than a poor man. I like the idea that the common man is able to obtain a position of power, regardless of background, but maybe I've watched Mr Smith Goes to Washington too many times.
I do agree that there's an issue with polarization, but I think that at the end of the day, you'll still have two candidates, and that you'll end up with polarization anyways. At the same time, I think there are problems with having too many candidate options, as I mentioned in my other post in this thread. Maybe 2 is too few, and 10 is too many, and theres a happy medium in the middle somewhere.